code: def maximum_flow(
      flowG, _s, _t, capacity="capacity", flow_func=None, **kwargs
  ):
      """Find a maximum single-commodity flow.
  
      Parameters
      ----------
      flowG : NetworkX graph
          Edges of the graph are expected to have an attribute called
          'capacity'. If this attribute is not present, the edge is
          considered to have infinite capacity.
  
      _s : node
          Source node for the flow.
  
      _t : node
          Sink node for the flow.
  
      capacity : string
          Edges of the graph G are expected to have an attribute capacity
          that indicates how much flow the edge can support. If this
          attribute is not present, the edge is considered to have
          infinite capacity. Default value: 'capacity'.
  
      flow_func : function
          A function for computing the maximum flow among a pair of nodes
          in a capacitated graph. The function has to accept at least three
          parameters: a Graph or Digraph, a source node, and a target node.
          And return a residual network that follows NetworkX conventions
          (see Notes). If flow_func is None, the default maximum
          flow function (:meth:`preflow_push`) is used. See below for
          alternative algorithms. The choice of the default function may change
          from version to version and should not be relied on. Default value:
          None.
  
      kwargs : Any other keyword parameter is passed to the function that
          computes the maximum flow.
  
      Returns
      -------
      flow_value : integer, float
          Value of the maximum flow, i.e., net outflow from the source.
  
      flow_dict : dict
          A dictionary containing the value of the flow that went through
          each edge.
  
      Raises
      ------
      NetworkXError
          The algorithm does not support MultiGraph and MultiDiGraph. If
          the input graph is an instance of one of these two classes, a
          NetworkXError is raised.
  
      NetworkXUnbounded
          If the graph has a path of infinite capacity, the value of a
          feasible flow on the graph is unbounded above and the function
          raises a NetworkXUnbounded.
  
      See also
      --------
      :meth:`maximum_flow_value`
      :meth:`minimum_cut`
      :meth:`minimum_cut_value`
      :meth:`edmonds_karp`
      :meth:`preflow_push`
      :meth:`shortest_augmenting_path`
  
      Notes
      -----
      The function used in the flow_func parameter has to return a residual
      network that follows NetworkX conventions:
  
      The residual network :samp:`R` from an input graph :samp:`G` has the
      same nodes as :samp:`G`. :samp:`R` is a DiGraph that contains a pair
      of edges :samp:`(u, v)` and :samp:`(v, u)` iff :samp:`(u, v)` is not a
      self-loop, and at least one of :samp:`(u, v)` and :samp:`(v, u)` exists
      in :samp:`G`.
  
      For each edge :samp:`(u, v)` in :samp:`R`, :samp:`R[u][v]['capacity']`
      is equal to the capacity of :samp:`(u, v)` in :samp:`G` if it exists
      in :samp:`G` or zero otherwise. If the capacity is infinite,
      :samp:`R[u][v]['capacity']` will have a high arbitrary finite value
      that does not affect the solution of the problem. This value is stored in
      :samp:`R.graph['inf']`. For each edge :samp:`(u, v)` in :samp:`R`,
      :samp:`R[u][v]['flow']` represents the flow function of :samp:`(u, v)` and
      satisfies :samp:`R[u][v]['flow'] == -R[v][u]['flow']`.
  
      The flow value, defined as the total flow into :samp:`t`, the sink, is
      stored in :samp:`R.graph['flow_value']`. Reachability to :samp:`t` using
      only edges :samp:`(u, v)` such that
      :samp:`R[u][v]['flow'] < R[u][v]['capacity']` induces a minimum
      :samp:`s`-:samp:`t` cut.
  
      Specific algorithms may store extra data in :samp:`R`.
  
      The function should supports an optional boolean parameter value_only. When
      True, it can optionally terminate the algorithm as soon as the maximum flow
      value and the minimum cut can be determined.
  
      Examples
      --------
      >>> G = nx.DiGraph()
      >>> G.add_edge("x", "a", capacity=3.0)
      >>> G.add_edge("x", "b", capacity=1.0)
      >>> G.add_edge("a", "c", capacity=3.0)
      >>> G.add_edge("b", "c", capacity=5.0)
      >>> G.add_edge("b", "d", capacity=4.0)
      >>> G.add_edge("d", "e", capacity=2.0)
      >>> G.add_edge("c", "y", capacity=2.0)
      >>> G.add_edge("e", "y", capacity=3.0)
  
      maximum_flow returns both the value of the maximum flow and a
      dictionary with all flows.
  
      >>> flow_value, flow_dict = nx.maximum_flow(G, "x", "y")
      >>> flow_value
      3.0
      >>> print(flow_dict["x"]["b"])
      1.0
  
      You can also use alternative algorithms for computing the
      maximum flow by using the flow_func parameter.
  
      >>> from networkx.algorithms.flow import shortest_augmenting_path
      >>> flow_value == nx.maximum_flow(G, "x", "y", flow_func=shortest_augmenting_path)[
      ...     0
      ... ]
      True
  
      """
      if flow_func is None:
          if kwargs:
              raise nx.NetworkXError(
                  "You have to explicitly set a flow_func if"
                  " you need to pass parameters via kwargs."
              )
          flow_func = default_flow_func
  
      if not callable(flow_func):
          raise nx.NetworkXError("flow_func has to be callable.")
  
      R = flow_func(
          flowG, _s, _t, capacity=capacity, value_only=False, **kwargs
      )
      flow_dict = build_flow_dict(flowG, R)
  
      return (R.graph["flow_value"], flow_dict)
  
file_path: networkx/networkx/algorithms/flow/maxflow.py
imports: import networkx
  from .boykovkolmogorov import boykov_kolmogorov
  from .dinitz_alg import dinitz
  from .edmondskarp import edmonds_karp
  from .preflowpush import preflow_push
  from .shortestaugmentingpath import shortest_augmenting_path
  from .utils import build_flow_dict
label_desc: Use image node_id 1 for calling a global function with example usage: maximum_flow(flowG, _s, _t, capacity, flow_func) and returns: R,  flow_dict